设M是作用在维数大于2的复可分 Hilbert空间H上的因子von Neumann代数. 证明了因子von Neumann代数M上的每一个非线性Lie 导子具有形式A→ φ(A)+h(A)I, 其中φ:M→M是可加的导子, h:M→C是非线性映射且对所有A,B∈M,有h(AB-BA)=0.
Abstract
Let M be a factor von Neumann algebra acting on a complex separable Hilbert space H with dim H > 2. We prove that every nonlinear Lie derivation on a factor von Neumann algebra M is of the form A → φ(A)+h(A)I, where φ : M → M is an additive derivation and h : M → C is a nonlinear map with h(AB-BA) = 0 for all A,B ∈ M.
关键词
Lie导子 /
非线性 /
von Neumann代数
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Key words
Lie derivation /
nonlinear /
von Neumann algebra
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参考文献
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脚注
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基金
国家自然科学基金资助项目(10571114);陕西省自然科学基础研究计划资助项目(2004A17)
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